Note 1 to entry: Defining a ray as the confined radiation exchange between two subtended surface area elements dA and dA′ at distance l, with normal vectors $n_A$ and ${n^{\prime }}_A$ and orientation angles θ and θ′ with respect to a common optical axis, the geometric extent is equal to the action of all possible rays between both surface areas A and A′. This is expressed by the integral over the product of all projected area elements dA cos θ and dA′ cos θ′ weighted by the distance squared to account for the apparent size of the subtending surfaces areas:

${\displaystyle G=\frac{1}{l^2}{\displaystyle \underset{A}{\int }{\displaystyle \underset{A^{\prime }}{\int }\text{d}A\cos \theta \cdot \text{d}{A}^{\prime }\cos {\theta }^{\prime }}}={\displaystyle \int \text{d}G}}$

with

${\displaystyle \text{d}G=\frac{\text{d}A\cos \theta \cdot \text{d}{A}^{\prime }\cos {\theta }^{\prime }}{l^2}=\text{d}A\cos \Theta \cdot \text{d}\Omega =\text{d}{A}^{\prime }\cos {\theta }^{\prime }\cdot \text{d}{\Omega }^{\prime }=\text{d}{G}^{\prime }}$

where dΩ and dΩ′ are the solid angle elements defining the angular extent of dA′ from dA and dA from dA′ respectively.

Note 2 to entry: "Single-pass" means that the term applies only for radiation transfer in a single defined direction. It does not apply to devices such as Fabry–Pérot cavities.

Note 3 to entry: See also "optical extent".

Note 4 to entry: The geometric extent is expressed in square metre times steradian (m²·sr).

Note 5 to entry: This entry was numbered 845-01-33 in IEC 60050-845:1987.